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Input-to-state stability of neutral type systems

100%

Gil' M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2013

tom 33

nr 1

5-16

We consider the system $ẋ(t) - ∫₀^{η} dR̃(τ) ẋ(t-τ) = ∫_0^{η} dR(τ)x(t-τ) + [Fx](t) + u(t)$ (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems, and the Ostrowski inequality for determinants.

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

75%

Ichalal D., Marx B., Ragot J., Maquin D.

International Journal of Applied Mathematics and Computer Science

2012

tom 22

nr 1

197-210

New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polya's theorem. Some simulation examples are given in order to illustrate the proposed approaches.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 International Journal of Applied Mathematics and Computer Science

1 Gil' M.

1 Ichalal D.

1 Maquin D.

1 Marx B.

1 Ragot J.

1 2013

1 2012

Wyniki wyszukiwania

Input-to-state stability of neutral type systems

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems